Modifications in the photoionization cross-section of a quantum dot with position-dependent effective mass

TL;DR

The paper addresses how a position-dependent effective mass in a quantum dot influences photoionization cross-sections. It develops a radial PDM Schrödinger formulation for $m(r)=\mu r^\gamma$ with a harmonic confinement, removes the first-derivative coupling to obtain an effective potential $V_{\mathrm{eff}}(r)$, and solves for eigenstates and energies. PCS is computed via a standard dipole-transition framework with a Lorentzian broadening, revealing strong sensitivity to $\gamma$ and the confinement parameter $\omega_0$, including inversion phenomena in certain regimes. The results suggest that engineering mass inhomogeneity provides a tunable handle to control optical transitions in quantum dots, with potential implications for optoelectronic devices and sensors.

Abstract

In this work, we investigate the photoionization cross-section of an electron confined in a quantum dot, considering the position-dependent variation of the effective mass through the parameter $γ$. We used a theoretical model based on the Schrödinger equation, in which $γ$ influences the energy levels and wave functions through an effective potential obtained from the harmonic oscillator potential - which, in the limit $γ= 0$, reduces to the original harmonic oscillator potential. Furthermore, we compared the modifications in the photoionization cross-section of these quantum systems with the constant-mass case. Our results demonstrate that even a small variation in $γ$ significantly impacts the photoionization process's amplitude and peak position. We also found that for specific values of $γ$, an inversion occurs: The amplitude, which initially increases as the quantum dot absorbs the photon, begins to decrease. Additionally, we observed that the optical transitions involving the ground state restrict the admissible values of $γ$ to negative values only. These results may have relevant implications for designing optoelectronic devices based on quantum dots with adjustable mass properties.

Figures (13)

• Figure 1: (Color online) Plots of the oscillator potential defined by Eq. \ref{['radp']} with a position-dependent mass, considering $\hbar\omega_0 = 30\,\mathrm{meV}$, for different values of $\gamma$: (a) $\gamma = -0.05$, (b) $\gamma = 0$, and (c) $\gamma = 0.05$.
• Figure 2: (Color online) Plots of the ratio between mass and effective mass of the electron as a function of position for different values of $\gamma$: in (a), $\gamma$ varies from 1.0 to 1.1; in (b), from 2.0 to 2.1.
• Figure 3: (Color online) The Figures (a), (b), (c), (d), (e), (f) depict the effective potential for fixed values of $\hbar\omega_{0} = 30$ meV, corresponding to quantum states $(n=0, \ell=0)$, $(n=0, \ell=1)$ , $(n=0, \ell=2)$ , $(n=1, \ell=0)$, $(n=1, \ell=1)$ and $(n=1, \ell=2)$, respectively, with the parameter $\gamma$ varying from -0.05 to 0.05 in intervals of 0.01.
• Figure 4: (Color online) The figures (a), (b), and (c) show the effective potential for the quantum states $(n=0, \ell=0)$, $(n=0, \ell=1)$, and $(n=0, \ell=2)$. Meanwhile, figures (d), (e), and (f) display the effective potential for the states $(n=1, \ell=0)$, $(n=1, \ell=1)$, and $(n=1, \ell=2)$. The graphs represent the effective potential as a function of $r$, considering $\hbar \omega_0$ varying from 0 to $50 ~ \mathrm{meV}$ in increments of $5~\mathrm{meV}$, with $\gamma=-0.1$.
• Figure 5: (Color online) Figure (a) shows the effective potential as a function of $r$ for negative $\gamma$ values ranging from $-0.11$ to $-0.01$, while Figure (b) presents the effective potential for positive $\gamma$ values in the range of $0$ to $0.10$. In both cases, $\hbar\omega_{0} = 30~\mathrm{meV}$ was considered. The analyzed configuration corresponds to the state $(n=0, \ell=0)$, resulting in a bound state only in case (a).